Study of the different flow patterns in the melting section of a co-rotating twin-screw extruder.
Polymer Engineering and Science - February 1, 2003
Guo Yichong
Word count: 5666. citation details
[pic]
INTRODUCTION
Twin-screw extrusion (TSE) Involves solid conveying, melting, mixing, venting and homogenizing, and the extrusion process affects the quality of polymer products considerably. Co-rotating twin-screw extruders are mainly used for compounding, and they are commonly of modular design, which means the screw elements can be configured to reach optimal conditions. Conveying elements and kneading blocks are the two common types of screw elements, which are designed based on conjugation or kinematics principles.
Investigations of co-rotating TSE have covered many aspects. Recent literature shows that some investigations first obtained data from experiments, and then obtained the regularity about the TSE process according to the experimental results (1-3). Such studies usually had some practicality, for instance, to clarify the temperature profiles, pressure drop, etc. Other investigations simulated the process with physical and mathematical methods, and then verified the simulation results with experimental data (4-9). They often emphasized the theoretical significance.
Several experimental methods have been used in TSE melting studies. Todd (10) conducted his experiments using a clam-shell barrel. Bawiskar and White (11) and Potente and Melish (12) adopted the screw extraction technique. Sakai (13), Liu et al. (14), and Liu and Zhu (15, 16) observed extrusion phenomena directly through glass windows that were fixed on the barrel. Research focused on various aspects. Bawiskar and White (17) established a melting model of co-rotating TSE involving screw elements and kneading disk elements. White et al. (18) calculated heat transfer coefficients and screw temperature profiles. They found that filling degree and screw size affected those coefficients. Wilczynski and White (19) did an experimental study of melting in a counter-rotating TSE. The work of Vergnes et al. (20) covered many factors influencing melting process, including processing conditions, screw parameters, screw configuration, and pellet size. Potente et al. (21) established a model for the melting of polymer ble nds. Potente et al. (22) also studied the morphology change of PP/PA6 blends in the melting section of a co-rotating TSE. They withdrew the screw after suddenly stopping the machine, and then took samples at different positions along the screws. These research studies have had both theoretical significance and practical value.
Visualization is a practical experimental technique for studying the polymer extrusion process. The technique has revealed great differences between the phenomena of TSE and those of single-screw extrusion, and it has been successfully used to demonstrate and verify the partially filled characteristics of the TSE process.
Melting is a key step. In the present work, we focused on the melting process. Using the visualization technique, we were able to identify that several flow patterns existed in the melting section of the screws. Each pattern was closely related to the degree of fill.
Based upon these observations, a concept for describing the different flow patterns In the melting section is Introduced.
THE WINDOWED TWIN-SCREW EXTRUDER (14)
A co-rotating twin-screw extruder with openings on its barrel was used In the present study. These openings are arranged at the top and left and right sides of the barrel. Special pieces of glass are fixed on every opening to form several windows on the barrel. Figure I is a schematic diagram of the barrel showing the window arrangement. Six windows are at the top side of the barrel to expose the intermeshing zone, and seven windows are alternatively arranged on the left and right sides to cover the whole axial length of the screws. Through the windows, researchers can observe the extrusion process directly with the naked eye. Monitoring and recording of the extrusion process using a camera are also made possible. It should be mentioned that the windows at the top side are numbered from TW1 to TW6, while the windows on the left and right sides are numbered from SW1 to SW7, as shown in Fig. 1. These numbers will be referred to later.
The transmission system, screws, feeders, motors and frame of this experimental machine are the same as m industrial machines. The extruder used in this study has screws of 50 mm diameter, with a 42 mm centerline distance. The L/D ratio of the screws is 28:1 and it has a maximum screw speed of 300 rpm.
THE DIFFERENCE IN THE FLOW PATTERNS IN THE MELTING SECTION OF TSE
Polymer materials flow in different patterns in the melting section of the screws, mainly because of different degrees of fill. No matter which pattern appears, a common characteristic is that the solid pellets adhere to each other with the melt film on their surfaces. In other words, the solid pellets disperse in the melt. This situation lasts throughout the whole melting process.
If the filling degree, [epsilon], is relatively low, the adjoining pellets adhere to each other to form individual groups at the end of the solid-conveying section. and then enter the melting section. Each group is described as two-phase cylinder group in Fig. 2. The melt surrounds the solid pellets, and the cylinder group rolls along the flight channel of the screws. As the melt develops, the solid changes into melt gradually, and finally vanishes; then, melting ends (14).
The present study focuses on high degrees of [epsilon], Higher [epsilon] means higher feeding ratio and higher throughput, as expected, and the investigation has practical significance. In this situation, a continuous polymer bed is formed, as shown in Fig. 3, instead of individual cylinder groups.
There are different continuous flow patterns under different conditions. In the present work, we conducted visualization extrusion experiments with high impact polystyrene (HIPS) powder and with low density polyethylene (LDPE) pellets. In the two processes the screw rotating speeds were the same, and the feeding ratios of the two processes were adjusted to obtain similar gravity throughputs. A continuous polymer bed appeared in both of the two processes, but there was a difference between them. The bulk density of the HIPS powder is less than that of the LDPE pellets, so the filling degree in the experiment with HIPS was higher. Figure 4 shows the phenomenon of the HIPS powder's melting. The arrow under the picture indicates the extrusion direction. The powder is not compressed closely in the flights, although the filling degree is higher. In our experiment, at the position where side window No. 4 (SW4) is located, the polymer has molten completely (Fig. 5). During the whole melting process, the polymer bed is always continuous.
Figure 6 shows the melting of pellets in the experiment. It is continuous, but sometimes it is discrete and then continuous again. This means the filling degree is slightly lower. Under this condition there will be more room in the screw flights.
Filling degree is a crucial factor determining which pattern may appear. In fact, the flow patterns in melting section change gradually from the two-phase cylinder groups to the continuous polymer bed as the filling degree increases gradually. According to the experimental phenomena we show this change in Fig. 7 (the intermeshing zone is not involved). In the experiment the melting section of the twin-screw consisted of screw elements only.
The two-phase cylinder groups are shown in Fig. 7a. When [epsilon] increases, the groups become bigger if there is no room limit in the screw flights. In fact, the groups are squeezed. They get a caterpillar-like shape, and roll forward down the flight channel (Fig. 7b). If [epsilon] gets a further increase, the size of the caterpillar-shaped group increases synchronously. When s reaches a certain degree, the rolling direction will change to the transverse direction of the flight channel; this is shown in Fig. 7c. If the [epsilon] increases again, the individual groups will touch each other, and a continuous bed forms, although sometimes it is discrete. The polymer bed rolls in the transverse direction of the flight channel while it moves down the channel. This situation is shown in Fig. 7d. When the screw flight is almost fully filled, that is to say, the value of [epsilon] increases to almost 1, the polymer bed will be continuous (Fig. 7e), but it is still not tightly compressed.
It is important to note the variety of the flow patterns in the melting process of TSE mentioned above. There are obvious differences between two-phase cylinder groups and the continuous bed. Before we establish a melting model, a certain flow pattern must be specified first, based on this variety conception.
Some points about TSE as follows:
1) There are different flow patterns in melting section in TSE because of different degrees of fill. These patterns can be classified into two categories: 1) discrete, as shown in Fig. 7a, b and c; and 2) continuous, as shown in Fig. 7d and e. Generally speaking, continuous flow patterns are expected because of their higher throughput.
2) Filling degree [epsilon] is a important factor that determines which pattern may occur. [epsilon] is influenced by many factors, such as feeding ratio, screw rotating speed, screw geometry, the degree of positive displacement, polymer properties, and screw configuration.
3) Melting phenomena in TSE show great differences from those in single-screw extrusion. In the melting section of a single-screw extruder, the melt accumulates in the front part of the flank and a melt reservoir forms gradually. In contrast, no melt reservoir forms in TSE, and there are frequent position exchanges between melt and solid, and the solid pellets always disperse in the melt. In single-screw extrusion, melting starts when the melt film appears close to the inner wall of the barrel, or a melt reservoir begins to form. For TSE, it is believed that the melt starts when the surfaces of the polymer pellets begin to melt, and therefore, the pellets adhere to each other. So the melting of a single pellet should be investigated. Powder can also be considered a type of pellet, but of smaller size. But powder is different from pellets when modeling and calculating the melting process because the size of the pellets has the same order of magnitude as that of the flight depth, while the size of a piece of po wder is much smaller.
4) Liu et al. (14) described two-phase cylinder groups, and this discrete type is shown in Fig. 7a. We summarized the flow pattern shown in Fig. 7d from Fig. 6, and the flow pattern shown in Fig. 7e from Figs. 4 and 5. The degree of fill changes gradually, as mentioned above, so there should be transitional flow patterns between the discrete type and the continuous type. We then deduced the types shown in Fig. 7b and c.
A MELTING MODEL FOR PROCESSING CRYSTALLINE POLYMER PELLETS IN A CO-ROTATING TSE
A model was established for the flow pattern shown in Fig. 7d, as an example of the variety conception mentioned above. LDPE pellets were used in the experiment. The property parameters are as follows: solid density [[rho].sub.s] 923 (kg/[m.sup.3]) melt density [[rho].sub.m] 853 (kg/[m.sup.3]) solid specific heat [C.sub.s] 2098 (J/(kg * K)) melt specific heat [C.sub.m] 2300 (J/(kg * K)) solid thermal conductivity [K.sub.s] 0.335 (W/(m * K))
Melt thermal conductivity [K.sub.m] 0.265 (W/(m * K)) melting latent heat [lambda] 1.298 x [10.sup.5] (J/kg)
The model is for the fully filled part, and the intermeshing zone is not involved. The melting section of the screws consisted of screw elements only, and no kneading disk block is employed.
Cartesian coordinates are used, as shown in Fig. 8a. H refers to the depth of the flight. The polymer bed moves along the flight channel at a speed Vz, and rolls at transverse direction of the channel. Figure 8b shows the transverse section of the bed. The solid pellets disperse in the melt. The pellets are simplified as cubes (Fig. 8c). When the velocity field of the melt was calculated, we neglected the cubes (Fig. 8d).
When the melting process of the solid pellets or cubes is concerned, we make several assumptions: 1) the six surfaces of every cube are always parallel to YZ, ZX, XY coordinate planes, respectively; 2) heat transfer takes place only along the Y direction; 3) melting of a individual cube has no effect on the others, so we need only study a single cube. Figure 9a shows this simplification; his the height of the cube at Y direction. According to assumption 2), the cube can be simplified further into a solid layer with a thickness of h, as shown in Fig. 9b. The solid layer divides the melt into an upper melt part and a lower melt part. The solid layer and the two melt parts form two solid-melt boundaries. They are called upper and lower melting surfaces, respectively. At the two surfaces, the temperature is always the melting point [T.sub.m].
At the beginning of melting, the upper melting surface is at a height of [a.sub.o] - H in the Y direction, where h/H [less than or equal to] 1. [a.sub.0] is a dimensionless parameter (Fig. 9b), and the lower melting surface is at a height of [a.sub.0] - H-h. The solid layer melts at the two surfaces simultaneously. After a time interval [tau] the upper surface moves to the height of au H along Y direction, and the lower surface moves to the height of [a.sub.L] - H (Fig. 10). [a.sub.u] and [a.sub.L] are dimensionless parameters that refer to the positions of upper and lower melting surface in Y direction, at the moment [tau]. O [less than or equal to] [a.sub.u] [less than or equal to] 1, 0 [less than or equal to] [a.sub.L] [less than or equal to] 1. When the two surfaces meet, the melting process ends.
Here the temperature fields of melt and solid, and the velocity fields of the melt should be solved. There are several more assumptions: 4) the melt is a Newtonian fluid; 5) all the velocity and temperature fields involved are steady: 6) [V.sub.y] = 0; 7) volume forces are neglected: and 8) the sum of the flow at the X direction equals zero.
The velocity field of melt (Fig. 8d). According to the assumptions, the Navier-Stokes equation in the X direction becomes
[[partial].sub.p]/[[partial].sub.x] = [mu] [[partial].sup.2] [[partial].sub.x]/[[partial].sub.y.sup.2] (1)
Where P is pressure (Pa), [mu] is viscosity (Pa.s). The boundary conditions are
[V.sub.x] = 0 when y = 0; (2a)
[V.sub.x] = [V.sub.2] when y = H. (2b)
Where [V.sub.2] is the relative velocity of the screw to the inner wall of the barrel in X direction.
The temperature field of melt. (Fig. 9b and 10). The energy equation is simplified as
[K.sub.m] [[partial].sup.2]T/[partial][Y.sup.2] + [mu] [([partial][V.sub.x] / [partial]y)].sup.2] (3)
Where [K.sub.m] is melt thermal conductivity (w/(m.K)), T refers to temperature. Equation 3 is applicable to both upper and lower melt part are:
T = [T.sub.b], when y = H; (4a)
T = [T.sub.m], when y = [[alpha].sub.U]H; ([[alpha].sub.L] [less than or equal to] [[alpha].sub.U] [less than or equal to] [[alpha].sub.0]). (4b)
Here [T.sub.b] is barrel temperature. The boundary conditions for lower melt part are:
T = [T.sub.m], when y = [[alpha].sub.L]H, ([[alpha].sub.0] - (h/H) [less than or equal to] [[alpha].sub.L] [less than or equal to] [[alpha].sub.U]); (5a)
T = [T.sub.s], when y = 0, (5b)
With [T.sub.s] represents the screw temperature. The temperature field of the melt [T.sub.1] can be solved with Eqs 1-5.
The temperature field of solid layer (Fig. 10). Because the temperature is always the melting point [T.sub.m] at upper and lower melting surfaces, there must be a thin layer (with height of [[alpha].sub.1]H, Fig. 10) where the temperature gradient is zero. This layer is most probably at the middle of the solid layer, and we call It center layer." So an equation of 2nd order presents the temperature field of the solid layer [T.sub.2]
[T.sub.2] = R[(y - [[alpha].sub.1]H).sup.2] + [t.sub.0] (6)
Where [[alpha].sub.1] = ([[alpha].sub.U] + [[alpha].sub.L])/2, R is a coefficient, [t.sub.0] is the temperature of the center layer which is located at the height of [[alpha].sub.1]H at the moment [tau].
After the temperature field of melt and solid are solved, we can solve the moving velocities of upper and lower melting surface according to the heat balance equation:
[q.sub.1] - [q.sub.2] = [q.sub.3] (7)
Where [q.sub.1] is the heat flow density that enters the melting surface from melt;
[q.sub.2] is the heat flow density that enters the solid layer from the surface;
[q.sub.3] is the heat consumed for melting at the surface per unit time and per unit area.
[q.sub.1], [q.sub.2] and [q.sub.3] are measured in (w/[m.sup.2]).
THE SOLUTIONS
The velocity field of melt. From Eqs 1, 2a and 2b, we get
[[upsilon].sub.x] = [V.sub.2]/H y + 1/2[mu] dp/dx ([y.sup.2] - Hy) (8)
From assumption 8, we induce [[integral].sup.H.sub.0] [[upsilon].sub.x]dy = 0, so dp/dx = 6[mu][V.sub.2]/[H.sup.2] (9)
Putting Eq 9 into 8, 23 get
[[upsilon].sub.x] = [V.sub.2]/H y (3 y/H - 2) (10)
[partial][v.sub.x]/[partial]y = 6[V.sub.2]/[H.sup.2] y - 2[V.sub.2]/H (11)
The temperature field on melt. We define
[N.sub.0] = [mu]/[K.sub.m] (12)
So Eq 3 becomes
[[partial].sup.2]T/[partial][y.sup.2] = - [N.sub.0] [([partial][[upsilon].sub.x]/[partial]y).sup.2] (13)
Putting Eq 11 into 13, and integrate it twice, we get
[T.sub.1] = -3 [N.sub.0] [V.sup.2.sub.2]/[H.sup.4][y.sup.4] + 4 [N.sub.0][V.sup.2.sub.2]/[H.sup.3][y.sup.3] -
2 [N.sub.0][V.sup.2.sub.2]/[H.sup.2] [y.sup.2] + [C.sub.1]y + [C.sub.2] (14)
Where [T.sub.1] refers to the temperature field of the melt. With Eqs 4a and 4b, the constants about upper melt part [C.sub.U1] and [C.sub.U2] corresponding to [C.sub.1] and [C.sub.2] in Eq 14) can be solved as:
[C.sub.U1] = [N.sub.0] [V.sup.2.sub.2](- 3 [[alpha].sup.4.sub.U] + 4 [[alpha].sup.3.sub.U] - 2 [[alpha].sup.2.sub.U] + 1) + [T.sub.b] - [T.sub.m]/H(1 - [[alpha].sub.U]) (15a)
[C.sub.U2] = [T.sub.b] + [N.sub.0] [V.sup.2.sub.2] -
[N.sub.0][V.sup.2.sub.2](- 3 [[alpha].sup.4.sub.U] + 4 [[alpha].sup.3.sub.U] - 2 [[alpha].sup.2.sub.U] + 1) + [T.sub.b] - [T.sub.m]/(1 - [[alpha].sub.U]) (15b)
Similarly, with Eqs 5a and 5b, the constants about lower melt part [C.sub.L1] and [C.sub.L2] are:
[C.sub.L1] = - [N.sub.0][V.sup.2.sub.2](- 3 [[alpha].sup.4.sub.L] + 4 [[alpha].sup.3.sub.L] - 2 [[alpha].sup.2.sub.L]) + [T.sub.m] - [T.sub.s]/[[alpha].sub.L]H (16a)
[C.sub.L2] = [T.sub.s] (16b)
The temperature field of solid layer. Assuming that at the beginning, the temperature of the center layer is [T.sub.0], and that the variation of center layer temperature [t.sub.0] is directly proportional to the position variations of upper and lower melting surfaces. So we get:
([[alpha].sub.U] - [[alpha].sub.L])H/h = [T.sub.m] - [t.sub.0]/[T.sub.m] - [T.sub.0] (17a)
[t.sub.0] = [T.sub.m] - ([[alpha].sub.U] - [[alpha].sub.L])H/h ([T.sub.m] - [T.sub.0]) (17b)
Putting Eq 17b into 6:
[T.sub.2] = R[(y - [[alpha].sub.1]H).sup.2] + [T.sub.m] - ([[alpha].sub.U] - [[alpha].sub.L])H/h ([T.sub.m] - [T.sub.0]) (18)
Where [T.sub.2] refers to the temperature field of the center layer. Take Eqs 4b or 5a as the boundary conditions of Eq 18, and we get
R = 4([T.sub.m] - [T.sub.0])/hH([[alpha].sub.U] - [[alpha].sub.L]) (19)
[T.sub.2] = 4([T.sub.m] - [T.sub.0])/hH([[alpha].sub.U] - [[alpha].sub.L])[(y - [[alpha].sub.1]H).sup.2] +
[T.sub.m] - ([[alpha].sub.U] - [[alpha].sub.L])H/h([T.sub.m] - [T.sub.0]) (19b)
The moving velocities of melting surfaces. After we know the temperature fields of melt and solid layer, the moving velocities of melting surfaces could be solved according to Eq 7. In Eq 7:
[q.sub.1] = - [K.sub.m]d[T.sub.1]/dy[\.sub.y = [alpha] * H]
[q.sub.2] = - [K.sub.s]d[T.sub.2]/dy[\.sub.y = [alpha] * H]
[q.sub.3] = V [[rho].sub.s][lambda]
So Eq 7 becomes:
[K.sub.m]d[T.sub.1]/dy[\.sub.y = [alpha] * H] - [K.sub.s]d[T.sub.2]/dy[\.sub.y = [alpha] * H] = - V[[rho].sub.s][lambda] (20)
Where [K.sub.s] refers to solid thermal conductivity (W/(m*K)): [[rho].sub.s] is solid density (kg/[m.sup.3]); [lambda] is melting latent heat of crystalline polymer (J/kg); V is moving velocities of melting surfaces along Y direction; [alpha] is either [[alpha].sub.U] or [[alpha].sub.L], according to the velocity of either upper or lower melting surfaces, that is going to be calculated.
The moving velocities of upper melting surfaces [V.sub.U]. According to Eq 14, we reason that: d[T.sub.1U]/dy[\.sub.y = [[alpha].sub.U]H] - 12 [[alpha].sup.3.sub.U][N.sub.0][V.sup.2.sub.2]/H +
12 [[alpha].sup.2.sub.U][N.sub.0][V.sup.2.sub.2]/H - 4 [[alpha].sub.U][N.sub.0][V.sup.2.sub.2]/H + [C.sub.U1] (21)
Where [T.sub.1U] refers to the temperature field of upper melt part. Put Eq 15a into Eq 21, and it becomes d[T.sub.1U]/dy[\.sub.y = [[alpha].sub.U] * H] = 1/H(1 - [[alpha].sub.U])
[[N.sub.0][V.sup.2.sub.2]A([[alpha].sub.U]) + ([T.sub.b] - [T.sub.m])] (22)
Where
A([[alpha].sub.U]) = (9[[alpha].sup.4.sub.U] - 20 [[alpha].sup.3.sub.U] + 14 [[alpha].sup.2.sub.U] - 4 [[alpha].sub.U] + 1). (23)
According to Eq 19b, we get: d[T.sub.2]/dy[\.sub.y = [[alpha].sub.U] * H] = 4([T.sub.m] - [T.sub.0])/h (24)
Putting Eqs 22 and 24 into 20, we get the moving velocities of upper melting surfaces [V.sub.U].
[V.sub.U] = V = - [[K.sub.m]/H(1 - [[alpha].sub.U])][[N.sub.0][V.sup.2.sub.2]A([[alpha].sub.U]) + ([T.sub.b] - [T.sub.m])] - [K.sub.S]4([T.sub.m] - [T.sub.0])/h/[rho]S[lambda] (25)
The moving velocities of lower melting surfaces [V.sub.L]. From Eq 14, we obtain d[T.sub.1L]/dy[\.sub.y = [[alpha].sub.L]H] =
- 12 [[alpha].sup.3.sub.L][N.sub.0][V.sup.2.sub.2]/H + 12 [[alpha].sup.2.sub.L][N.sub.0][V.sup.2.sub.2]/H - 4 [[alpha].sub.L][N.sub.0][V.sup.2.sub.2]/H + [C.sub.L1] (26)
Where [T.sub.1L] refers to the temperature field of lower melt part. Put Eq 16a into Eq 26, and it becomes d[T.sub.1L]/dy[\.sub.y = [[alpha].sub.L]H] = 1/[[alpha].sub.L]H [[N.sub.0][V.sup.2.sub.2]B([[alpha].sub.L]) + [T.sub.m] - [T.sub.s]] (27) where B([[alpha].sub.L]) = [[alpha].sup.2.sub.L](-9 [[alpha].sup.2.sub.L] + 8 [[alpha].sub.L] - 2). (28)
From Eq 19b, we get: d[T.sub.2]/dy[\.sub.y = [[alpha].sub.L]H] = - 4([T.sub.m] - [T.sub.0])/h (29)
Putting Eqs 27 and 29 into 20, we get the moving velocities of lower melting surfaces [V.sub.L].
[V.sub.L] = V = -
[[K.sub.m]/[[alpha].sub.L]H][[N.sub.0][V.sup.2.sub.2]B([[alpha].sub.L ]) + ([T.sub.m] - [T.sub.s])] + [K.sub.s] 4([T.sub.m] - [T.sub.0])/h/[[rho].sub.s][lambda]
Now the melting time, which is the time from the beginning to the terminating of melting, can be calculated. At any moment [tau], we calculate the velocities with Eqs 25 and 30. Within a time increment [DELTA][tau], these velocities are taken as average velocities. If [DELTA][tau] is short enough, the position variations of both upper and lower melting surfaces can be calculated precisely. When the two surfaces meet, the melting process terminates. The calculation has been programmed with C language. Figure 11 is the block diagram of the computer program. Table 1 lists the calculated results of melting time with different [[alpha].sub.0] values. A pellet changes its position in the screw flight during the extrusion process. When we calculate the melting time, it is fixed at the midway of the flight in Y direction (depth direction). The screw diameter of the machine is 50 mm, and the centerline distance is 42 mm, so the depth of the flight is 50 - 42 = 8 mm. We measured the diameter and height of the pellets i n our experiment. The average value of the diameter was 4.03 mm and that of the height was 2.59 mm. We assumed the height of the cube h was the average value of the two, say (4.03 + 2.59)/2 = 3.31 mm. When such a pellet is put in the flight and is at the midway, [[alpha].sub.0] is about 0.7 (see Fig, 10). Table 2 is the comparison of experimental data and calculated results with [[alpha].sub.0] = 0.7. The influence of the intermeshing zone is to speed the melting process. The model does not include this influence, and this is one of the reasons why there are deviations between experimental data and calculated results listed in Table 2.
CONCLUSIONS
The main purpose of the present work is to describe the different flow patterns in the melting section of a co-rotating TSE, and simultaneously to establish a melting model for one type of continuous flow pattern as an example, and then to get the time the melting process takes. This time datum is one of initial parameters for formulating the extrusion technique, especially, screw configuration.
Melting phenomena in TSE show great differences from those in single-screw extrusion. Solids (both pellets and powder) disperse in melt all the time at the melting section in a TSE. The melting of a single pellet should be investigated when the melting process of a TSE is considered.
The most important significance attached to the present work is that we have introduced the variety conception for flow patterns. The conception says there are different flow patterns in the melting section in a TSE and they can be classified as either discrete or continuous. Filling degree [epsilon] is an important factor that determines which pattern may appear. According to the conception, we should establish different models for each flow patterns identified. In practice, continuous patterns are expected to achieve to reach a higher throughput in a TSE.
Tabe 1

Calculated Results of Melting Time With [[alpha].sub.0] as Parameter
(S).

[[alpha].sub.0] 0.45 0.5 0.6 0.7 0.8 0.85 0.9

Screw rotating 10 27 35 40 42 39 34 23 speed 30 21 27 31 32 30 27 20
(r/min) 50 15 20 23 24 22 20 17

Table 2

Calculated and Experimental Results of Melting Time Under Different
Speeds (S).

Calculated Experimental results data
Screw rotating 10 42 35 speed (r/min) 30 32 23 50 24 17

ACKNOWLEDGMENT

The authors wish to express their gratitude to Dr. Anthony Chi-ying Wong of University of Hong Kong, Hong Kong, for his valuable suggestions and work for the revision of this paper.

NOMENCLATURE

[epsilon] filling degree
[[rho].sub.s] solid density (kg/[m.sup.3])
[[rho].sub.m] melt density (kg/[m.sup.3])
[K.sub.s] solid thermal conductivity (w/(m*K))
[K.sub.m] melt thermal conductivity (w/(m*K))
[lambda] melting latent heat (J/kg)
P pressure (Pa) m viscosity (Pa*s)
[V.sub.2] the relative velocity of the screw to the inner wall of the barrel in X direction (m/s)
[T.sub.b] barrel temperature (K)
[T.sub.s] screw temperature (K)
[T.sub.1] the temperature field of the m (K)
[T.sub.2] the temperature field of the solid layer (K)
[T.sub.1U] the temperature field of upper melt part (K)
[V.sub.U] the moving velocities of upper melting surfaces (m/s)
[T.sub.1L] the temperature field of lower melt part (K)
[V.sub.L] the moving velocities of lower melting surfaces (m/s)
REFERENCES
(1.) M. A. Huneault, M. F. Champagne, and A. Luciani, Polym. Eng. Sci, 36, 1694 (1996).
(2.) J. Cheng, Y. Xie, D, Bigio, A. Lee, and P. Andersen, "Characterization of Kneading Block Performance in Co-Rotating Twin-Screw Extruders," 56th (Vol. 1) Annu. Tech. Conf.--SPE, 60 (1998).
(3.) W. Michaeli and A. Grefenstein, Intern. Polymer Processing, 11, 121 (1996).
(4.) T. Avalosse and Y. Rubin, Intern. Polymer Processing, 15, 117 (2000).
(5.) D. Goffart, D. J. Van Der Wal, E. M. Klomp, H. W. Hoogstraten, L. P. B. M. Janssen, L. Breysse, and Y. Trolez, Polym. Eng. Set, 36, 901 (1996).
(6.) D. J. Van Der Wal, D. Goffart, E. M. Klomp, H. W. Hoogstraten, and L. P. B. M. Janssen, Polym. Eng. Sci, 36, 912 (1996).
(7.) J. L. White and Z. Chen, Polym. Eng. Sci., 34, 229 (1994).
(8.) M. A. Huneault and M. M. Dumoulin, 52nd (Vol. 1) Annu. Tech. Conf.--SPE, 327 (1994).
(9.) B. Kim and J. L. White, Polym. Eng. Sci., 37, 576 (1997).
(10.) B. D. Todd, Intern. Polymer Processing, 8, 113 (1993).
(11.) S. Bawiskar and J. L. White, Intern. Polymer Processing, 12, 131 (1997).
(12.) H. Potente and U. Melish, Intern. Polymer Processing, 11, 101 (1996).
(13.) T. Sakai, Adv. Polym. Tech., 14, 277 (1995).
(14.) T. Liu, A.C.-Y. Wong, and F. H. Zhu, Intern. Polymer Processing, 16, 113 (2001).
(15.) T. H. Liu and F. H. Zhu, Gaofenzi Cailiao Kexue Yu Gongcheng, 13 (5), 12 (1997).
(16.) T. H. Liu and F. H. Zhu, Gaofenzi Cailiao Kexue Yu Gongcheng, 13 (6), 33 (1997).
(17.) S. Bawiskar and J. L. White, Polym. Eng. Sci, 38, 727 (1998).
(18.) J. L. White, E. K. Kim, J. M. Keum, and H. C. Jung, Polym. Eng. Sci, 41, 1448 (2001).
(19.) K. Wilczynski and J. L. White, Intern. Polymer Processing, 16, 257(2001).
(20.) B. Vergnes, Q. Souveton, M. L. Delacour, and A. Ainser, Intern. Polymer Processing, 16, 351 (2001).
(21.) H. Potente, M. Bastian, J. Flecke, and D. Schramm, Intern. Polymer Processing, 16, 131 (2001).
(22.) H. Potente, M. Bastian, K. Bergemann, M. Senge, G. Scheel, and Th. Winkelmann, Polym. Eng. Sci, 222 (2001).

[pic]

Citation Details
Title: Study of the different flow patterns in the melting section of a co-rotating twin-screw extruder.
Author: Guo Yichong
Publication: Polymer Engineering and Science (Refereed)
Date: February 1, 2003
Publisher: Society of Plastics Engineers, Inc.
Volume: 43 Issue: 2 Page: 306(11)